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Question Number 157870 by Odhiambojr last updated on 29/Oct/21

$$findtheintegral:$$$$\int \left\{(3x+1)/(x^2+4)\right\}dx$$

Answered by puissant last updated on 29/Oct/21

$$\mathrm{\Omega }=\int \frac{3x+1}{x^2+4}dx=\int \frac{3x}{x^2+4}dx+\int \frac{dx}{x^2+4}$$$$=\frac{3}{2}\int \frac{2x}{x^2+4}dx+\int \frac{dx}{x^2+4}$$$$=\frac{3}{2}ln\mid x^2+4\mid +\frac{1}{2}arctan\left(\frac{x}{2}\right)+C..$$

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